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MULTIPLE POSITIVE SOLUTIONS OF RESONANT AND NON-RESONANT NON-LOCAL FOURTH-ORDER BOUNDARY VALUE PROBLEMS

Published online by Cambridge University Press:  09 December 2011

J. R. L. WEBB  and
M. ZIMA
J. R. L. WEBB
Affiliation:
School of Mathematics and Statistics, University of Glasgow, Glasgow G12 8QW, UK e-mail: [email protected]
M. ZIMA
Affiliation:
Institute of Mathematics, University of Rzeszów, 35-959 Rzeszów, Poland e-mail: [email protected]
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Abstract

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We study the existence of positive solutions for equations of the form where 0 < ω < π, subject to various non-local boundary conditions defined in terms of the Riemann–Stieltjes integrals. We prove the existence and multiplicity of positive solutions for these boundary value problems in both resonant and non-resonant cases. We discuss the resonant case by making a shift and considering an equivalent non-resonant problem.

Keywords

Primary 34B10secondary 34B1534B18
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 54 , Issue 1 , January 2012 , pp. 225 - 240
Copyright
Copyright © Glasgow Mathematical Journal Trust 2011

References

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